Free Statistics

of Irreproducible Research!

Author's title

Author*Unverified author*
R Software Modulerwasp_exponentialsmoothing.wasp
Title produced by softwareExponential Smoothing
Date of computationThu, 02 Jan 2014 08:14:35 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Jan/02/t1388668625t3i55mn2vkp413c.htm/, Retrieved Wed, 15 May 2024 12:38:06 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=232735, Retrieved Wed, 15 May 2024 12:38:06 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact156
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [(Partial) Autocorrelation Function] [] [2013-11-18 21:27:43] [cdd835b6be22d878f15dd5e149bcbc86]
- RMPD    [Exponential Smoothing] [] [2014-01-02 13:14:35] [12e977ea58b1a83461bd6217bf886aa8] [Current]
Feedback Forum

Post a new message
Dataseries X:
3.96
3.97
3.96
3.95
3.94
3.94
3.95
3.93
3.94
3.92
3.95
3.94
3.95
3.92
3.92
3.92
3.92
3.9
3.92
3.94
3.96
3.95
3.96
3.97
3.99
4
4.05
4.08
4.09
4.12
4.14
4.15
4.15
4.15
4.15
4.2
4.22
4.22
4.22
4.23
4.3
4.29
4.32
4.31
4.35
4.34
4.35
4.38
4.39
4.38
4.34
4.33
4.33
4.33
4.33
4.32
4.35
4.35
4.35
4.36
4.38
4.41
4.43
4.42
4.43
4.43
4.42
4.46
4.44
4.41
4.41
4.46
4.5
4.58
4.61
4.65
4.55
4.63
4.69
4.72
4.71
4.74
4.77
4.78




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232735&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232735&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232735&T=0

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 seconds
R Server'Gwilym Jenkins' @ jenkins.wessa.net







Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.987562367822681
beta0
gammaFALSE

\begin{tabular}{lllllllll}
\hline
Estimated Parameters of Exponential Smoothing \tabularnewline
Parameter & Value \tabularnewline
alpha & 0.987562367822681 \tabularnewline
beta & 0 \tabularnewline
gamma & FALSE \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232735&T=1

[TABLE]
[ROW][C]Estimated Parameters of Exponential Smoothing[/C][/ROW]
[ROW][C]Parameter[/C][C]Value[/C][/ROW]
[ROW][C]alpha[/C][C]0.987562367822681[/C][/ROW]
[ROW][C]beta[/C][C]0[/C][/ROW]
[ROW][C]gamma[/C][C]FALSE[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232735&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232735&T=1

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Estimated Parameters of Exponential Smoothing
ParameterValue
alpha0.987562367822681
beta0
gammaFALSE







Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.963.98-0.0200000000000005
43.953.97024875264355-0.0202487526435462
53.943.96025184653743-0.0202518465374304
63.943.95025188501814-0.0102518850181443
73.953.95012750917498-0.000127509174979945
83.933.96000158591222-0.0300015859122178
93.943.94037314869031-0.000373148690312686
103.923.95000464108616-0.0300046410861579
113.953.930373186689440.0196268133105577
123.943.95975588891523-0.0197558889152307
133.953.95024571647966-0.000245716479663649
143.923.96000305613119-0.0400030561311944
153.923.93049754329813-0.0104975432981287
163.923.93013056458231-0.0101305645823078
173.923.93012600023602-0.0101260002360237
183.93.93012594346636-0.0301259434663632
193.923.910374695403830.00962530459617028
203.943.929880284001840.0101197159981616
213.963.949874134694680.0101258653053238
223.953.96987405821186-0.0198740582118555
233.963.96024718622591-0.000247186225910134
243.973.97000307441136-3.07441135705133e-06
253.993.98000003823840.00999996176160201
2643.999875624153820.000124375846177749
274.054.009998453058970.040001546941026
284.084.059502475472620.0204975245273769
294.094.089745059329380.000254940670616932
304.124.099996829141710.0200031708582875
314.144.129751207918480.0102487920815149
324.154.149872529293830.000127470706171806
334.154.15999841456624-0.00999841456624395
344.154.16012435660273-0.0101243566027307
354.154.16012592302346-0.0101259230234572
364.24.160125942506020.0398740574939778
374.224.209504061139470.0104959388605268
384.224.2298694553731-0.00986945537309669
394.224.23012275265572-0.0101227526557208
404.234.23012590307415-0.000125903074152944
414.34.240001565936130.0599984340638722
424.294.3092537615459-0.0192537615458983
434.324.300239471204140.019760528795862
444.314.32975422581121-0.0197542258112078
454.354.320245695794590.0297543042054116
464.344.3596299269086-0.0196299269086015
474.354.35024414981056-0.000244149810557204
484.384.360003036645540.019996963354461
494.394.389751285125130.000248714874865108
504.384.39999690657587-0.0199969065758703
514.344.39024871416867-0.0502487141686743
524.334.35062497502421-0.020624975024214
534.334.34025652585302-0.0102565258530181
544.334.34012756689598-0.0101275668959779
554.334.3401259629519-0.0101259629519035
564.324.34012594300264-0.0201259430026361
574.354.330250319076290.0197496809237112
584.354.35975436073305-0.00975436073305147
594.354.36012132115092-0.0101213211509226
604.364.36012588526962-0.00012588526962265
614.384.370001565714680.00999843428531921
624.414.389875643152010.0201243568479903
634.434.419749700651720.0102502993482805
644.424.439872510547-0.0198725105469979
654.434.43024716697662-0.000247166976624413
664.434.44000307417194-0.0100030741719426
674.424.44012441455719-0.020124414557193
684.464.430250300066050.0297496999339542
694.444.46962998417484-0.0296299841748349
704.414.45036852684459-0.0403685268445866
714.414.42050208888843-0.0105020888884333
724.464.420130621118690.0398693788813125
734.54.469504119330340.0304958806696636
744.584.509620703453310.0703792965466921
754.614.589124648196650.0208753518033467
764.654.61974036005270.0302596399473014
774.554.65962364172852-0.109623641728517
784.634.561363458533760.0686365414662431
794.694.639146323943320.05085367605668
804.724.699367500682340.0206324993176574
814.714.72974338056259-0.0197433805625886
824.744.720245560905370.0197544390946263
834.774.749754301552670.0202456984473276
844.784.779748191449540.000251808550461696

\begin{tabular}{lllllllll}
\hline
Interpolation Forecasts of Exponential Smoothing \tabularnewline
t & Observed & Fitted & Residuals \tabularnewline
3 & 3.96 & 3.98 & -0.0200000000000005 \tabularnewline
4 & 3.95 & 3.97024875264355 & -0.0202487526435462 \tabularnewline
5 & 3.94 & 3.96025184653743 & -0.0202518465374304 \tabularnewline
6 & 3.94 & 3.95025188501814 & -0.0102518850181443 \tabularnewline
7 & 3.95 & 3.95012750917498 & -0.000127509174979945 \tabularnewline
8 & 3.93 & 3.96000158591222 & -0.0300015859122178 \tabularnewline
9 & 3.94 & 3.94037314869031 & -0.000373148690312686 \tabularnewline
10 & 3.92 & 3.95000464108616 & -0.0300046410861579 \tabularnewline
11 & 3.95 & 3.93037318668944 & 0.0196268133105577 \tabularnewline
12 & 3.94 & 3.95975588891523 & -0.0197558889152307 \tabularnewline
13 & 3.95 & 3.95024571647966 & -0.000245716479663649 \tabularnewline
14 & 3.92 & 3.96000305613119 & -0.0400030561311944 \tabularnewline
15 & 3.92 & 3.93049754329813 & -0.0104975432981287 \tabularnewline
16 & 3.92 & 3.93013056458231 & -0.0101305645823078 \tabularnewline
17 & 3.92 & 3.93012600023602 & -0.0101260002360237 \tabularnewline
18 & 3.9 & 3.93012594346636 & -0.0301259434663632 \tabularnewline
19 & 3.92 & 3.91037469540383 & 0.00962530459617028 \tabularnewline
20 & 3.94 & 3.92988028400184 & 0.0101197159981616 \tabularnewline
21 & 3.96 & 3.94987413469468 & 0.0101258653053238 \tabularnewline
22 & 3.95 & 3.96987405821186 & -0.0198740582118555 \tabularnewline
23 & 3.96 & 3.96024718622591 & -0.000247186225910134 \tabularnewline
24 & 3.97 & 3.97000307441136 & -3.07441135705133e-06 \tabularnewline
25 & 3.99 & 3.9800000382384 & 0.00999996176160201 \tabularnewline
26 & 4 & 3.99987562415382 & 0.000124375846177749 \tabularnewline
27 & 4.05 & 4.00999845305897 & 0.040001546941026 \tabularnewline
28 & 4.08 & 4.05950247547262 & 0.0204975245273769 \tabularnewline
29 & 4.09 & 4.08974505932938 & 0.000254940670616932 \tabularnewline
30 & 4.12 & 4.09999682914171 & 0.0200031708582875 \tabularnewline
31 & 4.14 & 4.12975120791848 & 0.0102487920815149 \tabularnewline
32 & 4.15 & 4.14987252929383 & 0.000127470706171806 \tabularnewline
33 & 4.15 & 4.15999841456624 & -0.00999841456624395 \tabularnewline
34 & 4.15 & 4.16012435660273 & -0.0101243566027307 \tabularnewline
35 & 4.15 & 4.16012592302346 & -0.0101259230234572 \tabularnewline
36 & 4.2 & 4.16012594250602 & 0.0398740574939778 \tabularnewline
37 & 4.22 & 4.20950406113947 & 0.0104959388605268 \tabularnewline
38 & 4.22 & 4.2298694553731 & -0.00986945537309669 \tabularnewline
39 & 4.22 & 4.23012275265572 & -0.0101227526557208 \tabularnewline
40 & 4.23 & 4.23012590307415 & -0.000125903074152944 \tabularnewline
41 & 4.3 & 4.24000156593613 & 0.0599984340638722 \tabularnewline
42 & 4.29 & 4.3092537615459 & -0.0192537615458983 \tabularnewline
43 & 4.32 & 4.30023947120414 & 0.019760528795862 \tabularnewline
44 & 4.31 & 4.32975422581121 & -0.0197542258112078 \tabularnewline
45 & 4.35 & 4.32024569579459 & 0.0297543042054116 \tabularnewline
46 & 4.34 & 4.3596299269086 & -0.0196299269086015 \tabularnewline
47 & 4.35 & 4.35024414981056 & -0.000244149810557204 \tabularnewline
48 & 4.38 & 4.36000303664554 & 0.019996963354461 \tabularnewline
49 & 4.39 & 4.38975128512513 & 0.000248714874865108 \tabularnewline
50 & 4.38 & 4.39999690657587 & -0.0199969065758703 \tabularnewline
51 & 4.34 & 4.39024871416867 & -0.0502487141686743 \tabularnewline
52 & 4.33 & 4.35062497502421 & -0.020624975024214 \tabularnewline
53 & 4.33 & 4.34025652585302 & -0.0102565258530181 \tabularnewline
54 & 4.33 & 4.34012756689598 & -0.0101275668959779 \tabularnewline
55 & 4.33 & 4.3401259629519 & -0.0101259629519035 \tabularnewline
56 & 4.32 & 4.34012594300264 & -0.0201259430026361 \tabularnewline
57 & 4.35 & 4.33025031907629 & 0.0197496809237112 \tabularnewline
58 & 4.35 & 4.35975436073305 & -0.00975436073305147 \tabularnewline
59 & 4.35 & 4.36012132115092 & -0.0101213211509226 \tabularnewline
60 & 4.36 & 4.36012588526962 & -0.00012588526962265 \tabularnewline
61 & 4.38 & 4.37000156571468 & 0.00999843428531921 \tabularnewline
62 & 4.41 & 4.38987564315201 & 0.0201243568479903 \tabularnewline
63 & 4.43 & 4.41974970065172 & 0.0102502993482805 \tabularnewline
64 & 4.42 & 4.439872510547 & -0.0198725105469979 \tabularnewline
65 & 4.43 & 4.43024716697662 & -0.000247166976624413 \tabularnewline
66 & 4.43 & 4.44000307417194 & -0.0100030741719426 \tabularnewline
67 & 4.42 & 4.44012441455719 & -0.020124414557193 \tabularnewline
68 & 4.46 & 4.43025030006605 & 0.0297496999339542 \tabularnewline
69 & 4.44 & 4.46962998417484 & -0.0296299841748349 \tabularnewline
70 & 4.41 & 4.45036852684459 & -0.0403685268445866 \tabularnewline
71 & 4.41 & 4.42050208888843 & -0.0105020888884333 \tabularnewline
72 & 4.46 & 4.42013062111869 & 0.0398693788813125 \tabularnewline
73 & 4.5 & 4.46950411933034 & 0.0304958806696636 \tabularnewline
74 & 4.58 & 4.50962070345331 & 0.0703792965466921 \tabularnewline
75 & 4.61 & 4.58912464819665 & 0.0208753518033467 \tabularnewline
76 & 4.65 & 4.6197403600527 & 0.0302596399473014 \tabularnewline
77 & 4.55 & 4.65962364172852 & -0.109623641728517 \tabularnewline
78 & 4.63 & 4.56136345853376 & 0.0686365414662431 \tabularnewline
79 & 4.69 & 4.63914632394332 & 0.05085367605668 \tabularnewline
80 & 4.72 & 4.69936750068234 & 0.0206324993176574 \tabularnewline
81 & 4.71 & 4.72974338056259 & -0.0197433805625886 \tabularnewline
82 & 4.74 & 4.72024556090537 & 0.0197544390946263 \tabularnewline
83 & 4.77 & 4.74975430155267 & 0.0202456984473276 \tabularnewline
84 & 4.78 & 4.77974819144954 & 0.000251808550461696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232735&T=2

[TABLE]
[ROW][C]Interpolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Observed[/C][C]Fitted[/C][C]Residuals[/C][/ROW]
[ROW][C]3[/C][C]3.96[/C][C]3.98[/C][C]-0.0200000000000005[/C][/ROW]
[ROW][C]4[/C][C]3.95[/C][C]3.97024875264355[/C][C]-0.0202487526435462[/C][/ROW]
[ROW][C]5[/C][C]3.94[/C][C]3.96025184653743[/C][C]-0.0202518465374304[/C][/ROW]
[ROW][C]6[/C][C]3.94[/C][C]3.95025188501814[/C][C]-0.0102518850181443[/C][/ROW]
[ROW][C]7[/C][C]3.95[/C][C]3.95012750917498[/C][C]-0.000127509174979945[/C][/ROW]
[ROW][C]8[/C][C]3.93[/C][C]3.96000158591222[/C][C]-0.0300015859122178[/C][/ROW]
[ROW][C]9[/C][C]3.94[/C][C]3.94037314869031[/C][C]-0.000373148690312686[/C][/ROW]
[ROW][C]10[/C][C]3.92[/C][C]3.95000464108616[/C][C]-0.0300046410861579[/C][/ROW]
[ROW][C]11[/C][C]3.95[/C][C]3.93037318668944[/C][C]0.0196268133105577[/C][/ROW]
[ROW][C]12[/C][C]3.94[/C][C]3.95975588891523[/C][C]-0.0197558889152307[/C][/ROW]
[ROW][C]13[/C][C]3.95[/C][C]3.95024571647966[/C][C]-0.000245716479663649[/C][/ROW]
[ROW][C]14[/C][C]3.92[/C][C]3.96000305613119[/C][C]-0.0400030561311944[/C][/ROW]
[ROW][C]15[/C][C]3.92[/C][C]3.93049754329813[/C][C]-0.0104975432981287[/C][/ROW]
[ROW][C]16[/C][C]3.92[/C][C]3.93013056458231[/C][C]-0.0101305645823078[/C][/ROW]
[ROW][C]17[/C][C]3.92[/C][C]3.93012600023602[/C][C]-0.0101260002360237[/C][/ROW]
[ROW][C]18[/C][C]3.9[/C][C]3.93012594346636[/C][C]-0.0301259434663632[/C][/ROW]
[ROW][C]19[/C][C]3.92[/C][C]3.91037469540383[/C][C]0.00962530459617028[/C][/ROW]
[ROW][C]20[/C][C]3.94[/C][C]3.92988028400184[/C][C]0.0101197159981616[/C][/ROW]
[ROW][C]21[/C][C]3.96[/C][C]3.94987413469468[/C][C]0.0101258653053238[/C][/ROW]
[ROW][C]22[/C][C]3.95[/C][C]3.96987405821186[/C][C]-0.0198740582118555[/C][/ROW]
[ROW][C]23[/C][C]3.96[/C][C]3.96024718622591[/C][C]-0.000247186225910134[/C][/ROW]
[ROW][C]24[/C][C]3.97[/C][C]3.97000307441136[/C][C]-3.07441135705133e-06[/C][/ROW]
[ROW][C]25[/C][C]3.99[/C][C]3.9800000382384[/C][C]0.00999996176160201[/C][/ROW]
[ROW][C]26[/C][C]4[/C][C]3.99987562415382[/C][C]0.000124375846177749[/C][/ROW]
[ROW][C]27[/C][C]4.05[/C][C]4.00999845305897[/C][C]0.040001546941026[/C][/ROW]
[ROW][C]28[/C][C]4.08[/C][C]4.05950247547262[/C][C]0.0204975245273769[/C][/ROW]
[ROW][C]29[/C][C]4.09[/C][C]4.08974505932938[/C][C]0.000254940670616932[/C][/ROW]
[ROW][C]30[/C][C]4.12[/C][C]4.09999682914171[/C][C]0.0200031708582875[/C][/ROW]
[ROW][C]31[/C][C]4.14[/C][C]4.12975120791848[/C][C]0.0102487920815149[/C][/ROW]
[ROW][C]32[/C][C]4.15[/C][C]4.14987252929383[/C][C]0.000127470706171806[/C][/ROW]
[ROW][C]33[/C][C]4.15[/C][C]4.15999841456624[/C][C]-0.00999841456624395[/C][/ROW]
[ROW][C]34[/C][C]4.15[/C][C]4.16012435660273[/C][C]-0.0101243566027307[/C][/ROW]
[ROW][C]35[/C][C]4.15[/C][C]4.16012592302346[/C][C]-0.0101259230234572[/C][/ROW]
[ROW][C]36[/C][C]4.2[/C][C]4.16012594250602[/C][C]0.0398740574939778[/C][/ROW]
[ROW][C]37[/C][C]4.22[/C][C]4.20950406113947[/C][C]0.0104959388605268[/C][/ROW]
[ROW][C]38[/C][C]4.22[/C][C]4.2298694553731[/C][C]-0.00986945537309669[/C][/ROW]
[ROW][C]39[/C][C]4.22[/C][C]4.23012275265572[/C][C]-0.0101227526557208[/C][/ROW]
[ROW][C]40[/C][C]4.23[/C][C]4.23012590307415[/C][C]-0.000125903074152944[/C][/ROW]
[ROW][C]41[/C][C]4.3[/C][C]4.24000156593613[/C][C]0.0599984340638722[/C][/ROW]
[ROW][C]42[/C][C]4.29[/C][C]4.3092537615459[/C][C]-0.0192537615458983[/C][/ROW]
[ROW][C]43[/C][C]4.32[/C][C]4.30023947120414[/C][C]0.019760528795862[/C][/ROW]
[ROW][C]44[/C][C]4.31[/C][C]4.32975422581121[/C][C]-0.0197542258112078[/C][/ROW]
[ROW][C]45[/C][C]4.35[/C][C]4.32024569579459[/C][C]0.0297543042054116[/C][/ROW]
[ROW][C]46[/C][C]4.34[/C][C]4.3596299269086[/C][C]-0.0196299269086015[/C][/ROW]
[ROW][C]47[/C][C]4.35[/C][C]4.35024414981056[/C][C]-0.000244149810557204[/C][/ROW]
[ROW][C]48[/C][C]4.38[/C][C]4.36000303664554[/C][C]0.019996963354461[/C][/ROW]
[ROW][C]49[/C][C]4.39[/C][C]4.38975128512513[/C][C]0.000248714874865108[/C][/ROW]
[ROW][C]50[/C][C]4.38[/C][C]4.39999690657587[/C][C]-0.0199969065758703[/C][/ROW]
[ROW][C]51[/C][C]4.34[/C][C]4.39024871416867[/C][C]-0.0502487141686743[/C][/ROW]
[ROW][C]52[/C][C]4.33[/C][C]4.35062497502421[/C][C]-0.020624975024214[/C][/ROW]
[ROW][C]53[/C][C]4.33[/C][C]4.34025652585302[/C][C]-0.0102565258530181[/C][/ROW]
[ROW][C]54[/C][C]4.33[/C][C]4.34012756689598[/C][C]-0.0101275668959779[/C][/ROW]
[ROW][C]55[/C][C]4.33[/C][C]4.3401259629519[/C][C]-0.0101259629519035[/C][/ROW]
[ROW][C]56[/C][C]4.32[/C][C]4.34012594300264[/C][C]-0.0201259430026361[/C][/ROW]
[ROW][C]57[/C][C]4.35[/C][C]4.33025031907629[/C][C]0.0197496809237112[/C][/ROW]
[ROW][C]58[/C][C]4.35[/C][C]4.35975436073305[/C][C]-0.00975436073305147[/C][/ROW]
[ROW][C]59[/C][C]4.35[/C][C]4.36012132115092[/C][C]-0.0101213211509226[/C][/ROW]
[ROW][C]60[/C][C]4.36[/C][C]4.36012588526962[/C][C]-0.00012588526962265[/C][/ROW]
[ROW][C]61[/C][C]4.38[/C][C]4.37000156571468[/C][C]0.00999843428531921[/C][/ROW]
[ROW][C]62[/C][C]4.41[/C][C]4.38987564315201[/C][C]0.0201243568479903[/C][/ROW]
[ROW][C]63[/C][C]4.43[/C][C]4.41974970065172[/C][C]0.0102502993482805[/C][/ROW]
[ROW][C]64[/C][C]4.42[/C][C]4.439872510547[/C][C]-0.0198725105469979[/C][/ROW]
[ROW][C]65[/C][C]4.43[/C][C]4.43024716697662[/C][C]-0.000247166976624413[/C][/ROW]
[ROW][C]66[/C][C]4.43[/C][C]4.44000307417194[/C][C]-0.0100030741719426[/C][/ROW]
[ROW][C]67[/C][C]4.42[/C][C]4.44012441455719[/C][C]-0.020124414557193[/C][/ROW]
[ROW][C]68[/C][C]4.46[/C][C]4.43025030006605[/C][C]0.0297496999339542[/C][/ROW]
[ROW][C]69[/C][C]4.44[/C][C]4.46962998417484[/C][C]-0.0296299841748349[/C][/ROW]
[ROW][C]70[/C][C]4.41[/C][C]4.45036852684459[/C][C]-0.0403685268445866[/C][/ROW]
[ROW][C]71[/C][C]4.41[/C][C]4.42050208888843[/C][C]-0.0105020888884333[/C][/ROW]
[ROW][C]72[/C][C]4.46[/C][C]4.42013062111869[/C][C]0.0398693788813125[/C][/ROW]
[ROW][C]73[/C][C]4.5[/C][C]4.46950411933034[/C][C]0.0304958806696636[/C][/ROW]
[ROW][C]74[/C][C]4.58[/C][C]4.50962070345331[/C][C]0.0703792965466921[/C][/ROW]
[ROW][C]75[/C][C]4.61[/C][C]4.58912464819665[/C][C]0.0208753518033467[/C][/ROW]
[ROW][C]76[/C][C]4.65[/C][C]4.6197403600527[/C][C]0.0302596399473014[/C][/ROW]
[ROW][C]77[/C][C]4.55[/C][C]4.65962364172852[/C][C]-0.109623641728517[/C][/ROW]
[ROW][C]78[/C][C]4.63[/C][C]4.56136345853376[/C][C]0.0686365414662431[/C][/ROW]
[ROW][C]79[/C][C]4.69[/C][C]4.63914632394332[/C][C]0.05085367605668[/C][/ROW]
[ROW][C]80[/C][C]4.72[/C][C]4.69936750068234[/C][C]0.0206324993176574[/C][/ROW]
[ROW][C]81[/C][C]4.71[/C][C]4.72974338056259[/C][C]-0.0197433805625886[/C][/ROW]
[ROW][C]82[/C][C]4.74[/C][C]4.72024556090537[/C][C]0.0197544390946263[/C][/ROW]
[ROW][C]83[/C][C]4.77[/C][C]4.74975430155267[/C][C]0.0202456984473276[/C][/ROW]
[ROW][C]84[/C][C]4.78[/C][C]4.77974819144954[/C][C]0.000251808550461696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232735&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232735&T=2

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Interpolation Forecasts of Exponential Smoothing
tObservedFittedResiduals
33.963.98-0.0200000000000005
43.953.97024875264355-0.0202487526435462
53.943.96025184653743-0.0202518465374304
63.943.95025188501814-0.0102518850181443
73.953.95012750917498-0.000127509174979945
83.933.96000158591222-0.0300015859122178
93.943.94037314869031-0.000373148690312686
103.923.95000464108616-0.0300046410861579
113.953.930373186689440.0196268133105577
123.943.95975588891523-0.0197558889152307
133.953.95024571647966-0.000245716479663649
143.923.96000305613119-0.0400030561311944
153.923.93049754329813-0.0104975432981287
163.923.93013056458231-0.0101305645823078
173.923.93012600023602-0.0101260002360237
183.93.93012594346636-0.0301259434663632
193.923.910374695403830.00962530459617028
203.943.929880284001840.0101197159981616
213.963.949874134694680.0101258653053238
223.953.96987405821186-0.0198740582118555
233.963.96024718622591-0.000247186225910134
243.973.97000307441136-3.07441135705133e-06
253.993.98000003823840.00999996176160201
2643.999875624153820.000124375846177749
274.054.009998453058970.040001546941026
284.084.059502475472620.0204975245273769
294.094.089745059329380.000254940670616932
304.124.099996829141710.0200031708582875
314.144.129751207918480.0102487920815149
324.154.149872529293830.000127470706171806
334.154.15999841456624-0.00999841456624395
344.154.16012435660273-0.0101243566027307
354.154.16012592302346-0.0101259230234572
364.24.160125942506020.0398740574939778
374.224.209504061139470.0104959388605268
384.224.2298694553731-0.00986945537309669
394.224.23012275265572-0.0101227526557208
404.234.23012590307415-0.000125903074152944
414.34.240001565936130.0599984340638722
424.294.3092537615459-0.0192537615458983
434.324.300239471204140.019760528795862
444.314.32975422581121-0.0197542258112078
454.354.320245695794590.0297543042054116
464.344.3596299269086-0.0196299269086015
474.354.35024414981056-0.000244149810557204
484.384.360003036645540.019996963354461
494.394.389751285125130.000248714874865108
504.384.39999690657587-0.0199969065758703
514.344.39024871416867-0.0502487141686743
524.334.35062497502421-0.020624975024214
534.334.34025652585302-0.0102565258530181
544.334.34012756689598-0.0101275668959779
554.334.3401259629519-0.0101259629519035
564.324.34012594300264-0.0201259430026361
574.354.330250319076290.0197496809237112
584.354.35975436073305-0.00975436073305147
594.354.36012132115092-0.0101213211509226
604.364.36012588526962-0.00012588526962265
614.384.370001565714680.00999843428531921
624.414.389875643152010.0201243568479903
634.434.419749700651720.0102502993482805
644.424.439872510547-0.0198725105469979
654.434.43024716697662-0.000247166976624413
664.434.44000307417194-0.0100030741719426
674.424.44012441455719-0.020124414557193
684.464.430250300066050.0297496999339542
694.444.46962998417484-0.0296299841748349
704.414.45036852684459-0.0403685268445866
714.414.42050208888843-0.0105020888884333
724.464.420130621118690.0398693788813125
734.54.469504119330340.0304958806696636
744.584.509620703453310.0703792965466921
754.614.589124648196650.0208753518033467
764.654.61974036005270.0302596399473014
774.554.65962364172852-0.109623641728517
784.634.561363458533760.0686365414662431
794.694.639146323943320.05085367605668
804.724.699367500682340.0206324993176574
814.714.72974338056259-0.0197433805625886
824.744.720245560905370.0197544390946263
834.774.749754301552670.0202456984473276
844.784.779748191449540.000251808550461696







Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
854.789996868097874.737509856104334.84248388009141
864.799996868097874.726229188900484.87376454729526
874.809996868097874.719838925794774.90015481040097
884.819996868097874.716000528611874.92399320758388
894.829996868097874.71379866375444.94619507244135
904.839996868097874.712761626286464.96723210990928
914.849996868097874.712608401242144.9873853349536
924.859996868097874.713155542541595.00683819365416
934.869996868097874.714275453522725.02571828267303
944.879996868097874.715875135766515.04411860042923
954.889996868097874.717884326167875.06210941002787
964.899996868097874.720248401746245.07974533444951

\begin{tabular}{lllllllll}
\hline
Extrapolation Forecasts of Exponential Smoothing \tabularnewline
t & Forecast & 95% Lower Bound & 95% Upper Bound \tabularnewline
85 & 4.78999686809787 & 4.73750985610433 & 4.84248388009141 \tabularnewline
86 & 4.79999686809787 & 4.72622918890048 & 4.87376454729526 \tabularnewline
87 & 4.80999686809787 & 4.71983892579477 & 4.90015481040097 \tabularnewline
88 & 4.81999686809787 & 4.71600052861187 & 4.92399320758388 \tabularnewline
89 & 4.82999686809787 & 4.7137986637544 & 4.94619507244135 \tabularnewline
90 & 4.83999686809787 & 4.71276162628646 & 4.96723210990928 \tabularnewline
91 & 4.84999686809787 & 4.71260840124214 & 4.9873853349536 \tabularnewline
92 & 4.85999686809787 & 4.71315554254159 & 5.00683819365416 \tabularnewline
93 & 4.86999686809787 & 4.71427545352272 & 5.02571828267303 \tabularnewline
94 & 4.87999686809787 & 4.71587513576651 & 5.04411860042923 \tabularnewline
95 & 4.88999686809787 & 4.71788432616787 & 5.06210941002787 \tabularnewline
96 & 4.89999686809787 & 4.72024840174624 & 5.07974533444951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=232735&T=3

[TABLE]
[ROW][C]Extrapolation Forecasts of Exponential Smoothing[/C][/ROW]
[ROW][C]t[/C][C]Forecast[/C][C]95% Lower Bound[/C][C]95% Upper Bound[/C][/ROW]
[ROW][C]85[/C][C]4.78999686809787[/C][C]4.73750985610433[/C][C]4.84248388009141[/C][/ROW]
[ROW][C]86[/C][C]4.79999686809787[/C][C]4.72622918890048[/C][C]4.87376454729526[/C][/ROW]
[ROW][C]87[/C][C]4.80999686809787[/C][C]4.71983892579477[/C][C]4.90015481040097[/C][/ROW]
[ROW][C]88[/C][C]4.81999686809787[/C][C]4.71600052861187[/C][C]4.92399320758388[/C][/ROW]
[ROW][C]89[/C][C]4.82999686809787[/C][C]4.7137986637544[/C][C]4.94619507244135[/C][/ROW]
[ROW][C]90[/C][C]4.83999686809787[/C][C]4.71276162628646[/C][C]4.96723210990928[/C][/ROW]
[ROW][C]91[/C][C]4.84999686809787[/C][C]4.71260840124214[/C][C]4.9873853349536[/C][/ROW]
[ROW][C]92[/C][C]4.85999686809787[/C][C]4.71315554254159[/C][C]5.00683819365416[/C][/ROW]
[ROW][C]93[/C][C]4.86999686809787[/C][C]4.71427545352272[/C][C]5.02571828267303[/C][/ROW]
[ROW][C]94[/C][C]4.87999686809787[/C][C]4.71587513576651[/C][C]5.04411860042923[/C][/ROW]
[ROW][C]95[/C][C]4.88999686809787[/C][C]4.71788432616787[/C][C]5.06210941002787[/C][/ROW]
[ROW][C]96[/C][C]4.89999686809787[/C][C]4.72024840174624[/C][C]5.07974533444951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=232735&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=232735&T=3

As an alternative you can also use a QR Code:  

The GUIDs for individual cells are displayed in the table below:

Extrapolation Forecasts of Exponential Smoothing
tForecast95% Lower Bound95% Upper Bound
854.789996868097874.737509856104334.84248388009141
864.799996868097874.726229188900484.87376454729526
874.809996868097874.719838925794774.90015481040097
884.819996868097874.716000528611874.92399320758388
894.829996868097874.71379866375444.94619507244135
904.839996868097874.712761626286464.96723210990928
914.849996868097874.712608401242144.9873853349536
924.859996868097874.713155542541595.00683819365416
934.869996868097874.714275453522725.02571828267303
944.879996868097874.715875135766515.04411860042923
954.889996868097874.717884326167875.06210941002787
964.899996868097874.720248401746245.07974533444951



Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ;
Parameters (R input):
par1 = 12 ; par2 = Double ; par3 = additive ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
if (par2 == 'Single') K <- 1
if (par2 == 'Double') K <- 2
if (par2 == 'Triple') K <- par1
nx <- length(x)
nxmK <- nx - K
x <- ts(x, frequency = par1)
if (par2 == 'Single') fit <- HoltWinters(x, gamma=F, beta=F)
if (par2 == 'Double') fit <- HoltWinters(x, gamma=F)
if (par2 == 'Triple') fit <- HoltWinters(x, seasonal=par3)
fit
myresid <- x - fit$fitted[,'xhat']
bitmap(file='test1.png')
op <- par(mfrow=c(2,1))
plot(fit,ylab='Observed (black) / Fitted (red)',main='Interpolation Fit of Exponential Smoothing')
plot(myresid,ylab='Residuals',main='Interpolation Prediction Errors')
par(op)
dev.off()
bitmap(file='test2.png')
p <- predict(fit, par1, prediction.interval=TRUE)
np <- length(p[,1])
plot(fit,p,ylab='Observed (black) / Fitted (red)',main='Extrapolation Fit of Exponential Smoothing')
dev.off()
bitmap(file='test3.png')
op <- par(mfrow = c(2,2))
acf(as.numeric(myresid),lag.max = nx/2,main='Residual ACF')
spectrum(myresid,main='Residals Periodogram')
cpgram(myresid,main='Residal Cumulative Periodogram')
qqnorm(myresid,main='Residual Normal QQ Plot')
qqline(myresid)
par(op)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Estimated Parameters of Exponential Smoothing',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Parameter',header=TRUE)
a<-table.element(a,'Value',header=TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,fit$alpha)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,fit$beta)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'gamma',header=TRUE)
a<-table.element(a,fit$gamma)
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Interpolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Observed',header=TRUE)
a<-table.element(a,'Fitted',header=TRUE)
a<-table.element(a,'Residuals',header=TRUE)
a<-table.row.end(a)
for (i in 1:nxmK) {
a<-table.row.start(a)
a<-table.element(a,i+K,header=TRUE)
a<-table.element(a,x[i+K])
a<-table.element(a,fit$fitted[i,'xhat'])
a<-table.element(a,myresid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Extrapolation Forecasts of Exponential Smoothing',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'t',header=TRUE)
a<-table.element(a,'Forecast',header=TRUE)
a<-table.element(a,'95% Lower Bound',header=TRUE)
a<-table.element(a,'95% Upper Bound',header=TRUE)
a<-table.row.end(a)
for (i in 1:np) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,p[i,'fit'])
a<-table.element(a,p[i,'lwr'])
a<-table.element(a,p[i,'upr'])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable2.tab')